I have both part 61 and 141 students- private and instrument (never done a 141 multi). For the private, there's essentially no difference. For the IFR, part 141 gives you a lot more time with the CFI, but you have less total time.

I'd say do either one for your private, and do your IFR part 61. That way you get to go explore the country and build some real PIC experience- not having a CFI there to hold your hand really does lots for your decision making ability. You may even scare yourself once or twice.